1. Field of the Invention
The invention relates to a method of correcting range migration (RM) in image generation in synthetic aperture radar.
2. Description of the Prior Art
Synthetic aperture radar (SAR) is an active microwave imaging method. A radar transmitting-receiving apparatus usually carried by an aircraft or satellite coherently records the echoes of high-frequency signals transmitted with a pulse repetition frequency (PRF). The antenna centre axis is usually aligned approximately perpendicularly to the trajectory.
FIG. 1 shows schematically how an individual point P in the scene to be imaged is acquired during the flyby of a sensor S. It will be assumed that the point P at the time t=0 has a minimum distance r from the sensor S. If a transmitted pulse is denoted in each case by EQU p(.tau.).multidot.exp{j.multidot..omega..sub.0 .multidot..tau.},(1)
wherein p(.tau.) is the complex envelope and .omega..sub.0 the radar carrier frequency, then the received echo at a predetermined instant t is a time-delayed version of said pulse: ##EQU1## wherein c is the velocity of light and R(t;r) the respective distance of the point P from the sensor S. In the simplified geometry of FIG. 1 R(t;r) has the following functional form: ##EQU2## wherein the velocity of the sensor S is denoted by v. The echoes received are coherently demodulated in the sensor S, i.e. the carrier frequency is eliminated. The point response of the SAR sensor is thus ##EQU3## wherein .lambda.=2 .pi.c/.omega..sub.0 is the radar wavelength.
These echoes are usually digitized and stored in a socalled raw data matrix. For example, the column direction corresponds to the echo travelling time .tau. (frequently also denoted as "range") and the row direction is the flight time t (also referred to as "azimuth").
The conversion of these raw data to a high-resolution image of the radar backscatter coefficients of the earth's surface is referred to as "focussing" or "compression" and today is usually carried out by special hardware or alternatively by digital computers, the socalled "SAR processors". This compression can be performed by correlation of the raw data with the point response given in equation (4). A direct implementation of this correlation in the time domain requires very intensive computations because the correlation kernel is both two-dimensional and range-dependent. From the argument of the impulse envelope p(.) in equation (4) it is clear that the echoes occur with varying time t at respective different echo times ##EQU4##
This effect is referred to as "range migration" (RM). Both the range migration and the phase term in equation (4) are range-dependent.
To carry out the compression more effectively as regards computing time, different frequency domain methods are employed. In the area of precision processing two methods are established: The socalled "range-Doppler" method, described inter alia by J. R. Bennett and I. G. Cumming in the publication "A Digital Processor for the Production of SEASAT Synthetic Aperture Radar Imgery" ESA-SP-154, December 1979 and the socalled "Wavenumber domain" processor, described by F. Rocca, C. Prati and A. Monti Guarnieri in the report "New Algorithms for Processing SAR Data", Esrin Contract 7998/88/F/FL(SC), 1989. A description and a comparison of these two methods will be found in "A Systematic Comparison of SAR Focussing Algorithms" by R. Bamler, in: Proc. IGARSS'91, pages 1005-1009, 1991.
The range-Doppler method is aimed at eliminating the effect of the RM so as to enable the correlation to be carried out thereafter only along straight lines .tau.=const. with the aid of a fast convolution (FFT). The latter operation is referred to as "azimuth compression". The RM correction here is carried out in the socalled range-Doppler domain which is formed by Fourier transformation of the raw data in the azimuth direction. The frequency f occurring here and corresponding to t is referred to as "Doppler frequency". The RM correction in the range-Doppler domain is possible because the echo energy in the range-Doppler domain is likewise concentrated along a curved line: ##EQU5##
The function a(f) can be determined with the aid of the approximation of the stationary phase. For the quadratic approximation of R(t;r) in equation (3) the following is for example obtained: ##EQU6##
The range migration correction is done by range-variant shift along the negative .tau. direction by the amount: ##EQU7## so that the entire echo energy is concentrated in the straight line .tau.=2.r/c=const.
In FIG. 2 range migration lines of three points each with a minimum distance r.sub.1, r.sub.2 and r.sub.3 respectively, from the sensor and the straight lines .tau.=2.r.sub.1,2,3 /c are given; in FIG. 2 the abscissa represents the Doppler frequency f and the ordinate the range time .tau.. The shifts .DELTA..tau. for a frequency f are also entered.
The shift distance is not generally an integer multiple of the range sampling interval. Consequently, the data must be interpolated in the range direction. This is an operation requiring a great deal of computing time and with the usually employed short interpolation kernels can lead to disturbances in the image.
To avoid the interpolation in the range-Doppler method it is possible to shift each range column completely by an amount corresponding to an integer multiple of the range sampling interval. This can be done by simple reindexing of the sample values. In this case an uncompensated range migration remains of magnitude: ##EQU8## wherein r is the value of r for which the range migration was just completely corrected.
In the wavenumber domain processor, firstly a two-dimensional range-invariant correlation is carried out utilizing the FFT, the range parameter r in equation (4) being assumed to be r=r.sub.0 =const. Thereafter, or optionally therebefore, the range variance of the correlation kernel is taken into account in that the phase term in equation (4) is corrected for each range sample value. Thus, with this procedure the range migration is exactly corrected only for r=r.sub.0, for example in the centre of the range swath; towards the edge of the range domain a residual range migration remains.
In a publication by K. Raney and B. Vachon "A Phase Preserving SAR Processor" in: Proc. IGARSS'89, pages 2588-2591, 1989, in which an improvement of the wavenumber domain processor is proposed, this residual range migration in the range-Doppler domain is eliminated by a shift similar to that in the range-Doppler method; this can however lead to the already mentioned interpolation problems. In the range-Doppler domain the residual shift to be performed is given by: ##EQU9##
In the publication by Rocca et al. mentioned at the beginning a wavenumber domain processor is proposed in which the range migration is completely corrected. For this purpose a socalled "Stolt interpolation" must be applied to the two-dimensional Fourier transform of the data. However, this interpolation impairs the image quality even more than the range migration correction in the range-Doppler domain.
In the SAR focussing methods hitherto employed the range migration is either not completely corrected or an explicit interpolation is carried out. The latter requires a great deal of computing time and can lead to disturbances in the focussed image.
The invention has its objective in the provision of a method for avoiding the aforementioned difficulties and providing a method for the correction of residual correction of range migration in image generation in synthetic aperture radar without carrying out an explicit interpolation of the data.
The invention therefore proposes a method for correcting range migration in image generation in synthetic aperture radar the improvement in which the eliminating the entire range migration, which in the range-Doppler domain is described by ##EQU10## wherein .DELTA..tau. is the desired echo time shift, r the minimum distance of a point from the radar and f the azimuth (Doppler) frequency, a residual range migration which is left by a focussing means and is described by ##EQU11## wherein .tau.' is any desired reference echo time, or for carrying out a Stolt interpolation before a range compression the acquired SAR raw data are transformed in an azimuth FFT unit to the range-Doppler domain; thereafter the data transformed to the range-Doppler domain are subjected in a multiplying unit to a multiplication by a two-dimensional phase function EQU exp{j.multidot..pi..multidot.k.multidot.a(f).multidot.(.tau.-.tau.'.sup.2 {
wherein k is the frequency modulation rate of a chirp pulse transmitted by the radar and .tau. the echo travelling time: after an additional range Fourier transformation on the azimuth-transformed data in a second multiplying unit a range compression is carried out with a modified range transfer function ##EQU12## wherein .nu. is the range frequency corresponding to the echo travelling time .tau., and finally with data transformed back to the range-Doppler domain by means of an inverse range FFT unit in a further multiplying unit a phase error is corrected by multiplication by the function EQU exp{-j.multidot..pi..multidot.a(f).multidot.(l+a(f)).multidot.k.multidot.(. tau.-.tau.').sup.2 }
Advantageous further developments of the method according to the invention are set forth in the subsidiary claims.